L1 ⚛ L1-071 ⊙ Testnet

Digital Holography (off-axis and in-line intensity holograms)

Coherent Imaging · Interferometric complex-field recovery

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⬇ L1-071.md

# ⚛ L1 Principle — Digital Holography (off-axis and in-line intensity holograms) **ID:** `L1-071` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Coherent Imaging — *Interferometric complex-field recovery* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** complex 2D > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554169 --- ## 🧠 1. Introduction **Digital Holography (off-axis and in-line intensity holograms)** is a **linear inverse problem** whose unknown lives in **complex 2D** space, within the **Interferometric complex-field recovery** sub-domain of **Coherent Imaging**. Measurements consist of photons collected by an optical detector via a **interferometric** sensing mechanism. The forward operator applies, in order: L · modulation · reference operator; L · add coherent operator; phase is lost; only intensity is measured; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson shot noise from quantum-limited detection. Off-axis single-shot: ill-posed without spatial bandwidth separation (tilt must exceed twice max object spatial frequency). In-line phase-shifting: well-posed with N >= 3 phase steps; stability dominated by reference-phase calibration error and wavelength drift. ## ⚙ 2. Forward Model Physical chain: **x** → L · modulation · reference → L · add coherent → Magnitude-squared → Spatial integration → **y** (detector). ``` y = ∫_A dA |·|² `L.add_coherent` `L.modulation.reference` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.modulation.reference` | L · modulation · reference operator | | `L.add_coherent` | L · add coherent operator | | `L.modulus_squared` | Phase is lost; only intensity is measured | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Coherent Imaging | | Sub domain | Interferometric complex-field recovery | | Carrier | photon | | Problem class | linear_inverse | | Solution space | complex_2D | | Noise model | shot_poisson | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3.3 | ## 📡 4. Measurement Model Off-axis single-shot: ill-posed without spatial bandwidth separation (tilt must exceed twice max object spatial frequency). In-line phase-shifting: well-posed with N >= 3 phase steps; stability dominated by reference-phase calibration error and wavelength drift. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | phase_L2_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `complex_field_recovery` · **Forward operator:** `off_axis_digital_hologram` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | Z mm | mm | 100 | | Photon count | — | 1000 | | Wavelength nm | nm | 632.8 | | Tilt angle mrad | — | 10 | | Wavelength drift | — | 0 | | Reference tilt error | — | 0 | | Propagation distance error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | Z mm | mm | 1.0 – 500.0 | | Photon count | — | 10 – 50000 | | Wavelength nm | nm | 400 – 1550 | | N phase shifts | — | 3 – 8 | | Tilt angle mrad | — | 1.0 – 50.0 | | Wavelength drift | — | 0.0 – 0.002 | | Phase shift error | — | 0.0 – 0.1 | | Reference tilt error | — | 0.0 – 2.0 | | Propagation distance error | — | 0.0 – 5.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 32.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 18.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xd93b970467e3ac7a98b365b06ed1fe861772605ba4604d3789d07ce52bdcc821` - **Chain tx hash:** `0xa034295c686077a8ba8f7cf6230b4614efbf784b9d7edad609f8501e5a632d68` - **Chain block:** `41554169` --- ## File Mapping This bundle consists of: `L1-071.md`, `L1-071.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-071.md` | Source of truth — edit this | Human or LLM | | `L1-071.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-071`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-071.md).
Regenerate L1-071.json so every field matches the Markdown.
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L2-071-001 Off-Axis Digital Holography Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554169,
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  "chain_tx_hash": "0xa034295c686077a8ba8f7cf6230b4614efbf784b9d7edad609f8501e5a632d68",
  "domain": "Coherent Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 1200,
    "metric": "PSNR_dB",
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    "regime": "Off-axis single-shot: ill-posed without spatial bandwidth separation (tilt must exceed twice max object spatial frequency). In-line phase-shifting: well-posed with N \u003e= 3 phase steps; stability dominated by reference-phase calibration error and wavelength drift.",
    "secondary": "phase_L2_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Coherent Imaging",
    "integration_axis": "spatial",
    "noise_model": "shot_poisson",
    "primitives": [
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      "L.add_coherent",
      "L.modulus_squared",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "interferometric",
    "solution_space": "complex_2D",
    "sub_domain": "Interferometric complex-field recovery",
    "title": "Digital Holography (off-axis and in-line intensity holograms)"
  },
  "size_tiers": {
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      "phase_shift_error"
    ],
    "allowed_problem_classes": [
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      "phase_imaging"
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    "center_spec": {
      "epsilon_fn_center": "32.0 dB PSNR",
      "forward_operator": "off_axis_digital_hologram",
      "input_format": "single_intensity_hologram_plus_reference_params",
      "omega": {
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        "W": 1024,
        "photon_count": 1000,
        "propagation_distance_error": 0.0,
        "reference_tilt_error": 0.0,
        "tilt_angle_mrad": 10.0,
        "wavelength_drift": 0.0,
        "wavelength_nm": 632.8,
        "z_mm": 100.0
      },
      "problem_class": "complex_field_recovery"
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    "epsilon_bounds": {
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        42.0
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        4096
      ],
      "N_phase_shifts": [
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        8
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      "W": [
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      ],
      "phase_shift_error": [
        0.0,
        0.1
      ],
      "photon_count": [
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      ],
      "propagation_distance_error": [
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      ],
      "reference_tilt_error": [
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      "tilt_angle_mrad": [
        1.0,
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      ],
      "wavelength_drift": [
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        0.002
      ],
      "wavelength_nm": [
        400,
        1550
      ],
      "z_mm": [
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      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Interferometric complex-field recovery",
  "title": "Digital Holography (off-axis and in-line intensity holograms)"
}

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